Why are black hole singularities stable?

The Friedmann equations says that huge matter densities lead to huge expansion rates. In Newtonian gravity, two massive point particles separated by an infinitesimal distance will experience an enormous force.

So what is different about a black hole?

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The Friedmann equations says that huge matter densities lead to huge expansion rates. Not true. And irrelevant in any case because the Friedmann equations don't apply to a black hole. In Newtonian gravity, two massive point particles separated by an infinitesimal distance will experience an enormous force. The force is attractive, so what's the problem? – Ben Crowell Nov 19 '14 at 7:00

The black hole singularities are of two types:

1. Spacelike--- this is only for nonrotating uncharged black hole
2. Timelike--- exact solutions for everything else, rotating charged
3. Cauchy horizon--- this is a makeshift fix to get rid of 2 and turn it into 1, which is introduced in an ad-hoc way by Penrose (he wants a spacelike singularity, and doesn't get it in the exact solutions). It isn't really third option.

For the spacelike singularities, they are in the future of any point in the interior, so they are not a location, but a time. They should not be thought of as an infinitely dense source of gravity, but rather an endpoint to the interior continuation, where from the string point of view, the infalling matter has totally thermalized.

For the timelike singularities, they have a diverging stress tensor, but they are not exactly ordinary singularities. They repel ordinary matter, and only light can touch them. If you shine light on them, they uncompress it, which is required for the solution to continue into the future (by the method of proof of Penroses' theorem--- the geodesics inside the horizon are all converging, and only a singularity can convert them to diverging).

This behavior has no non-relativistic analog. The picture of the singularity as a point of infinite density is only half-way accurate for a neutral black hole, which is completely non-generic as far as classical solutions go.

I must add than in my opinion, it is only the timelike singularities which are physical, the spacelike neutral Scwarzschild singularity is an artifact of high symmetry, and turns into a timelike singularity under generic perturbations. I also believe because of this that stuff goes into a black hole, and out again, after a traversal.

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What do you mean by " I also believe because of this that stuff goes into a black hole, and out again, after a traversal."? Out where? – FrankH Oct 11 '12 at 3:57
@FrankH: Out of the same horizon it fell in. This is coming out of the past-horizon extension of the black hole solution, and I believe this is what happens because I can't make sense of AdS/CFT without it, but I am still not certain how long the in-out takes. It's what happens classically, except classically, the in-out takes infinite time, so might as well be to another universe. I gave some answers about this idea here, it is probably original to me, but I didn't work it out in detail, although I will someday (unless someone beats me to it, or I die first). – Ron Maimon Oct 11 '12 at 17:59
Thanks! You definitely have interesting ideas... – FrankH Oct 11 '12 at 19:19